It is possible to obtain an O-1 visa without having worked for big companies, but it would require demonstrating extraordinary ability or achievement in the sciences, arts, education, business, or athletics. The O-1 visa is for individuals who have a demonstrated record of extraordinary ability in their field and who will continue to work in their field of expertise while in the United States.
If you are not able to demonstrate that you have worked for big companies, you will need to provide evidence of your extraordinary ability in your field, such as recognition from experts in your field, publications, awards, and other accomplishments.
It is also important to note that O-1 visa application process is highly complex and requires extensive documentation.